Date of this Version
Journal of Sound and Vibration (1996) 196(5), 635-658
In this work the dynamic response is considered of a homogeneous, fully clamped rectangular plate subject to spatially uniform thermal loads and narrow-band acoustic excitation. In both the pre- and post-buckled regimes, the small amplitude, linear response is confirmed. However, the primary focus is on the large amplitude, non-linear, snap-through response, because of the obvious implications for fatigue in aircraft components. A theoretical model is developed which uses nine spatial modes and incorporates initial imperfections and non-ideal boundary conditions. Because of the higher order nature of this model, it is inherently more complicated than a one-mode buckled beam equation (Duffing’s equation). An experimental system was developed to complement the theoretical results, and also to measure certain system parameters for the model which are not available theoretically. Several analysis techniques are used to characterize the response. These include time series, power spectra and autocorrelation functions. In addition, the fractal dimension and Lyapunov exponents for the response are computed to address the issue of spatial dimension and temporal complexity (chaos), respectively. Comparisons between theory and experiment are made and show considerable agreement. However, these comparisons also serve to point out difficulties in computing the fractal dimension and Lyapunov exponents from experimental data.